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Simplifying 11x2 + -24x + 12 = 0 Reorder the terms: 12 + -24x + 11x2 = 0 Solving 12 + -24x + 11x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. 1.090909091 + -2.181818182x + x2 = 0 Move the constant term to the right: Add '-1.090909091' to each side of the equation. 1.090909091 + -2.181818182x + -1.090909091 + x2 = 0 + -1.090909091 Reorder the terms: 1.090909091 + -1.090909091 + -2.181818182x + x2 = 0 + -1.090909091 Combine like terms: 1.090909091 + -1.090909091 = 0.000000000 0.000000000 + -2.181818182x + x2 = 0 + -1.090909091 -2.181818182x + x2 = 0 + -1.090909091 Combine like terms: 0 + -1.090909091 = -1.090909091 -2.181818182x + x2 = -1.090909091 The x term is -2.181818182x. Take half its coefficient (-1.090909091). Square it (1.190082645) and add it to both sides. Add '1.190082645' to each side of the equation. -2.181818182x + 1.190082645 + x2 = -1.090909091 + 1.190082645 Reorder the terms: 1.190082645 + -2.181818182x + x2 = -1.090909091 + 1.190082645 Combine like terms: -1.090909091 + 1.190082645 = 0.099173554 1.190082645 + -2.181818182x + x2 = 0.099173554 Factor a perfect square on the left side: (x + -1.090909091)(x + -1.090909091) = 0.099173554 Calculate the square root of the right side: 0.314918329 Break this problem into two subproblems by setting (x + -1.090909091) equal to 0.314918329 and -0.314918329.Subproblem 1
x + -1.090909091 = 0.314918329 Simplifying x + -1.090909091 = 0.314918329 Reorder the terms: -1.090909091 + x = 0.314918329 Solving -1.090909091 + x = 0.314918329 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.090909091' to each side of the equation. -1.090909091 + 1.090909091 + x = 0.314918329 + 1.090909091 Combine like terms: -1.090909091 + 1.090909091 = 0.000000000 0.000000000 + x = 0.314918329 + 1.090909091 x = 0.314918329 + 1.090909091 Combine like terms: 0.314918329 + 1.090909091 = 1.40582742 x = 1.40582742 Simplifying x = 1.40582742Subproblem 2
x + -1.090909091 = -0.314918329 Simplifying x + -1.090909091 = -0.314918329 Reorder the terms: -1.090909091 + x = -0.314918329 Solving -1.090909091 + x = -0.314918329 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.090909091' to each side of the equation. -1.090909091 + 1.090909091 + x = -0.314918329 + 1.090909091 Combine like terms: -1.090909091 + 1.090909091 = 0.000000000 0.000000000 + x = -0.314918329 + 1.090909091 x = -0.314918329 + 1.090909091 Combine like terms: -0.314918329 + 1.090909091 = 0.775990762 x = 0.775990762 Simplifying x = 0.775990762Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.40582742, 0.775990762}
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